This really is not a UA issue. Unless some number of jurisdictions accept a common format (which individual carriers could, of course, adopt), a "passport" is useless.
If and when a given jurisdiction opens to those who have been vaccinated and establishes a standard for proving that, the concept of whether a UA or AA or other carrier app may be useful. For the moment, not worth it.
Ultimately, I am betting that this will come down to a visa-like stamp in a passport. Subject to forgery, of course, but a very serious crime in most countries to do so.